Multiwfn forum

dcjskea

Member

Registered: 2019-11-29

Posts: 6

Electron Density Surfaces For Individual Localised Orbitals

I am studying chemical bonding in small molecules using localized orbitals. I use Multiwfn to calculate the localized data (.fchk file input, .fch file output). I use the output file with, for example, IQMol to calculate and visualize localized orbital surfaces (that is, the wavefunction surfaces).

I would now like to calculate and visualize the electron density (wavefunction squared) surfaces for each localized orbital. I do not know how to do this. I would be grateful for any assistance you could give. Thank you.

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,770

Website

Re: Electron Density Surfaces For Individual Localised Orbitals

The easiest way is: Performing orbital localization first, and then enter main function 0, in the menu select "Other settings" - "Choose plotting wavefunction or density" - "Density". Then if you select an orbital, the orbital probability density will be shown as isosurface map.

If you really want to use third-part software to visualize the orbital probability density, you should:
(1) Performing orbital localization
(2) Enter main function 6, use subfunction 26 to set occupation of all orbitals to 0, and then set occupation of the orbital of interest to 1. Return to main menu
(3) Using main function 5 to calculate grid data of electron density, in this case electron density corresponds to probability density of the orbital. Then export the grid data as .cub file in the post-processing menu.
(4) Use VMD, VESTA, ChimeraX and so on to visualize the isosurface based on the .cub file (I am not a IQmol user, I don't know if it supports .cub file)

dcjskea

Member

Registered: 2019-11-29

Posts: 6

Re: Electron Density Surfaces For Individual Localised Orbitals

Thank you for your reply. It has been very helpful. I would like to ask you to clarify some of the terminology you are using. I think it is important to get this right in my mind. From my understanding we have different parameters:

A Orbital (wavefunction) - a number, plus or minus
B electron density (wavefunction squared) - electrons per unit volume, e / Angstrom^3 ??
C electron probability density function (4 x pi x r^2 x psi^2 x dr) - a number, probability

Using Multiwfn, if I choose to calculate and visualize a "wavefunction" surface, what are the units of the isovalue I choose? Many visualization programs have the units as e / Angstrom^3 (electrons per cubic Angstrom). Is that true of Multiwfn?

Using Multiwfn, if I choose to calculate and visualize your "Density" surface, do you mean B or C? And what are the units of the isovalue in this case?

I hope my questions make sense. I look forward to your reply. Many thanks and regards.

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,770

Website

Re: Electron Density Surfaces For Individual Localised Orbitals

There are two common units of electron density (B), including a.u. (1/Bohr^3) and 1/Angstrom^3. Multwfn always uses the former.

According to the unit you given for C, C should be referred to as radial density function of electron density, and should never be confused with electron probability density function.

Orbital wavefunction is dimensionless. However, if someone forces you to give it a unit, according to Born's probability interpretation of wavefunction, the unit may be sqrt(1/Bohr^3).

The word "orbital density" or "orbital probability density" always corresponds to B.

dcjskea

Member

Registered: 2019-11-29

Posts: 6

Re: Electron Density Surfaces For Individual Localised Orbitals

Many thanks for your reply. Once again, it has been very helpful. If I may, I have a few more questions relating to isovalue units.

Using Multiwfn, I have been visualizing wavefunction surfaces using an isovalue of 0.05. If I then switch to your electron density surface, I notice that the isovalue defaults to a much smaller value. Could you explain the change in isovalue? And please confirm the units of your isovalues in both cases.

In trying to understand wavefunction visualization, I have compared the visual outputs from Multiwfn and another software (IQMol). I guess this may be a difficult task since the output is very sensitive to the isovalue, and the computation methods may be different. I find that wavefunction visualizations from IQMol (at isovalue 0.05 / Angstrom^3) correspond very closely to visualizations from Multiwfn (at isovalue 0.03 / Bohr^3). I can't make sense of this, assuming your units are /Bohr^3. Perhaps IQMol is not the best?

In the past I have used different visualization software - Avogadro, IQMol, VMD, Molden, wxMacMolPlt, Gabedit - some with success, others not. I would be interested in your views on the subject of visualization - is it a science, or more of an art?

Thank you. Best regards.

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,770

Website

Re: Electron Density Surfaces For Individual Localised Orbitals

The suitable isovalue(s) for visualizing grid data is different for different functions and purposes. For example, the Bader's definition of molecular vdW surface (in gas phase) corresponds to isosurface of electron density with isovalue of 0.001 a.u.; so , if you visualize rho=0.001 a.u. isosurface (note that the "rho" in this context is total electron density rather than probability density of an orbital), the vdW profile can be understood. You can also visualize such as rho=0.05 a.u. isosurface, but it doesn't have a known meaning.

As I noted, orbital wavefunction is dimensionless. If you visualize orbital wavefunction in Multiwfn, VMD, GaussView, chemcraft... with the same isovalue, then you will see exactly the same isosurface. I am not a IQmol user so I am unable to comment it.

dcjskea

Member

Registered: 2019-11-29

Posts: 6

Re: Electron Density Surfaces For Individual Localised Orbitals

Thank you for your reply. I think I now understand that isovalues are different depending on the parameter being visualized. For Multiwfn, can you confirm:

When plotting wavefunction, the units of the isovalue are (effectively) sqrt(1/Bohr^3)

When plotting electron density, the units of the isovalue are 1/Bohr^3

Please, now, forgive me for asking this question: is there a way of visualizing the radial electron density function surfaces (4 x pi x r^2 x psi^2) for an atom or molecule?

Many thanks. Regards.